一种对称损失函数下反向帕累托分布形状参数的估计  

Estimation of the Shape Parameter of the Reverse Pareto Distribution Under the Weighted p, q Symmetric Loss Function

作　　者：徐宝[1] 蓝海 赵仲达 Xu Bao;Lan Hai;Zhao Zhongda(College of Mathematics and Computer Science,Jilin Normal University,Siping 136000,China)

机构地区：[1]吉林师范大学数学与计算机学院,吉林四平136000

出　　处：《南开大学学报（自然科学版）》2023年第1期76-81,共6页Acta Scientiarum Naturalium Universitatis Nankaiensis

基　　金：国家自然科学基金(11571138)。

摘　　要：使用加权p,q对称损失函数研究了反向帕累托分布的形状参数在刻度参数给定条件下Bayes估计的形式与性质.得到了形状参数的Bayes估计的一般形式以及在给定共轭先验下的精确形式,证明了所得Bayes估计具有可容许性以及最小最大性.最后通过模拟研究了所得估计的返真性,结果表明,基于适当的p,q对称损失函数得出Bayes估计返真性较高.The forms and properties of the shape parameter in the reverse Pareto distribution with the given scale parameter are studied by the p,q weighted symmetric entropy loss function. The general form and the precise form of the Bayes estimation under the given conjugate prior distribution are obtained.Then, the Bayes estimation that obtained is proved to be the admissible and minimax estimation of the shape parameter. Finally, a small simulation investigation is conducted to evaluate the performance of the Bayesian estimation, the results show that the Bayes estimation which obtained is better on the recovering the parameter under the proper p,q weighted symmetric entropy loss function.

关 键 词：反向帕累托分布 损失函数 BAYES估计 可容许性 最小最大性 

分 类 号：O212.8[理学—概率论与数理统计]